# [racket] 80-bit precision in Racket

On Sun, Nov 11, 2012 at 03:11:50PM +0400, Dmitry Pavlov wrote:
>* Neil, Matthias,
*>*
*>* Certainly not #2, and I doubt that #4 is a problem for us
*>* (although it may be, buried somewhere in specific calculations).
*>*
*>* #1 and #3 definitely are our case. We are doing numerical
*>* integration of celestial bodies over large periods of time
*>* (100 years is a norm). The forces that act on bodies may be of
*>* quite different orders of magnitude: for example, for near-Earth
*>* objects the acceleration towards the Sun is about 2.9e-4 AU/days^2,
*>* while corrections for peculiar relativistic effects (Lense-Thirring
*>* acceleration etc.) can be as small as 1e-17 AU/days^2 (I do not
*>* have exact numbers now). And those effects must be taken
*>* into account. Yet the numerical integration procedure has its
*>* numerical inaccuracies, too. So when we integrate these
*>* accelerations over ten or more years, it sort of pushes the
*>* limit of double precision representation. Again, I do not
*>* (yet) have a precise mathematical proof of it, but it is
*>* more or less obvious that we need to try 80-bit at least.
*
Is it conceivable that you need multiple-precision fixed-point?
-- hendrik